This thesis investigates the teaching of mathematics at university level in London, and in particular by Augustus De Morgan (1806-1871) during his period as founder professor of mathematics at London University (later University College London) from 1828 to 1867. An examination of De Morgan's life and professorial career is followed by a review of changes in instruction at the college under his successors, together with a survey of higher mathematical tuition at other university-level institutions in the capital up to the turn of the twentieth century. Particular attention is paid to original teaching material and the set of students who later achieved distinction in mathematics and other disciplines.\ud A key feature of the research undertaken for this project has been its intensive use of previously unpublished archival documents, hitherto mostly unstudied. Consequently, much of the information which has been gleaned from these sources (such as De Morgan's lecture material, student notes and contemporary correspondence) has never appeared in print before. The data thus derived has been used in conjunction with publications from the period, as well as more recent works, to produce a contribution to the history of mathematical education which gives a more complete picture of how well nineteenth-century London was served for mathematical instruction than was previously available.\ud Previous studies of De Morgan have mainly concentrated on his work in algebra and logic, with little or no reference to his mathematical teaching, while published histories of relevant institutions (e. g. University College, University of London) are similarly localised, with few comparisons being drawn with other bodies, and almost no reference to mathematical tuition. By concentrating on the work of De Morgan as a teacher in the context of London mathematics, this thesis will attempt to fill these two important gaps in the literature.